Convergence of the partial sum of wavelet expansions and Gibbs phenomenon
Cao Huai-xin · Basic Sciences Journal of Textile Universities · 2007
The convergence of the partial sums of wavelet expansions at jumping points and Gibbs phenomenon are discussed in this paper.First,by studying the producing kernel,equivalent positions of the relation between the convergence of partial sums of wavelet expansions at jumping points and producing kernel are given.Then,by advanced studying of the partial sums of the wavelet expansions,equivalent theorems of relation between the convergence of the partial sums of wavelet expansions at jumping points and Gibbs phenomenon are established.